Mobile Robots Pose Tracking-A Set-membership Approach using a Visibility Information.

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion

Mobile Robots Pose Tracking

A Set-Membership Approach Using a Visibility Information

Rémy G UYONNEAU - Sébastien L AGRANGE - Laurent H ARDOUIN

University of Angers - LISA

30

^th

July 2012

Rémy Guyonneau - [email protected] University of Angers - LISA

Mobile Robots Pose Tracking - A Set-Membership Approach Using a Visibility Information 1 / 23

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Why...

... localization ?

• Important issue in mobile robotics

• Basic requirement for many autonomous tasks

• Mapping

• Path planning

• Object localization...

... visibility information ?

• To process a team localization

• Can a weak information lead to a localization ?

• To improve classical localization precision and robustness

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Why...

... localization ?

• Important issue in mobile robotics

• Basic requirement for many autonomous tasks

• Mapping

• Path planning

• Object localization...

... visibility information ?

• To process a team localization

• Can a weak information lead to a localization ?

• To improve classical localization precision and robustness

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Summary

1 The Pose Tracking Problem

2 The Visibility Information

3 The LUVIA algorithm

4 Conclusion

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Summary

1 The Pose Tracking Problem The robots

The objective

The set-membership approach 2 The Visibility Information

3 The LUVIA algorithm

4 Conclusion

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The robots

The robots

Robots

• Mobile wheeled robots : r _i

• Team of m robots : R ⁼ ^{r 1 ,· · · ,r i ,· · · ,r m }

Localization

• Pose = position and orientation

• q _i = (x _i , θ i ) , x _i = (x _i

₁

, x i

₂

)

• θ

i

given by a compass

Robots’ dynamic

• q i (k + 1) = f (q i (k),u i (k))

• k : discrete time

• u _i : the input vector (associated to the odometry)

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The robots

Robots

• Mobile wheeled robots : r _i

• Team of m robots : R ⁼ ^{r 1 ,· · · ,r i ,· · · ,r m }

Localization

• Pose = position and orientation

• q _i = (x _i , θ i ) , x _i = (x _i

₁

, x i

₂

)

• θ

i

given by a compass

Robots’ dynamic

• q i (k + 1) = f (q i (k),u i (k))

• k : discrete time

• u _i : the input vector (associated to the odometry)

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The robots

Robots

• Mobile wheeled robots : r _i

• Team of m robots : R ⁼ ^{r 1 ,· · · ,r i ,· · · ,r m }

Localization

• Pose = position and orientation

• q _i = (x _i , θ i ) , x _i = (x _i

₁

, x i

₂

)

• θ

i

given by a compass

Robots’ dynamic

• q i (k + 1) = f (q i (k),u i (k))

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The objective

Example of pose tracking

Initial pose

• The initial pose ( k = 0 ) is known

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Example of pose tracking

From time k = 0 to k = 1

• The robot explores the environment

• And computes its new pose q i (1) = f (q i (0),u i (0))

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Example of pose tracking

From time k = 0 to k = 1

• The robot explores the environment

• And computes its new pose q i (1) = f (q i (0), u i (0))

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Example of pose tracking

From time k = 1 to k = 2

• The robot continues its mission

• And computes its new pose q i (2) = f (q i (1),u i (1))

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Example of pose tracking

From time k = 1 to k = 2

• The robot continues its mission

• And computes its new pose q i (2) = f (q i (1), u i (1))

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Example of pose tracking

From time k = k _f − 1 to k = k _f

• And so on until the end of the mission k = k _f

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The drifting problem

Adding the odometry error

• During this pose tracking process the robot drifts

• u i (k) is not known but approximated (odometry)

A solution

• Known environment (map...)

• To use an exteroceptive information

• LIDAR sensor

• Landmark recognition

• A measurement vector y i (k)

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The drifting problem

Adding the odometry error

• During this pose tracking process the robot drifts

• u i (k) is not known but approximated (odometry)

A solution

• Known environment (map...)

• To use an exteroceptive information

• LIDAR sensor

• Landmark recognition

• A measurement vector y i (k)

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The set-membership approach

Example of set-membership pose tracking

Initial pose

• The initial box is given q i (0) ∈ [q i (0)]

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Example of set-membership pose tracking

Initial pose

• The initial box is given q i (0) ∈ [q i (0)]

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Example of set-membership pose tracking

From time k = 0 to k = 1

• The robot explores the environment

• The input vector is evaluated : u i (0) ∈ [u i (0)]

• The robot’s new pose : [q i (1)] = f ([q i (0)],[u i (0)])

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Example of set-membership pose tracking

From time k = 0 to k = 1

• The robot explores the environment

• The input vector is evaluated : u i (0) ∈ [u i (0)]

• The robot’s new pose : [q i (1)] = f ([q i (0)],[u i (0)])

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Example of set-membership pose tracking

From time k = 0 to k = 1

• The robot explores the environment

• The input vector is evaluated : u i (0) ∈ [u i (0)]

• The robot’s new pose : [q i (1)] = f ([q i (0)],[u i (0)])

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Example of set-membership pose tracking

From time k = 1 to k = 2

• The robot explores the environment

• The input vector is evaluated : u i (1) ∈ [u i (1)]

• The robot’s new pose : [q i (2)] = f ([q i (1)],[u i (1)])

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Example of set-membership pose tracking

From time k = 1 to k = 2

• The robot explores the environment

• The input vector is evaluated : u i (1) ∈ [u i (1)]

• The robot’s new pose : [q i (2)] = f ([q i (1)],[u i (1)])

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Example of set-membership pose tracking

From time k = 1 to k = 2

• The robot explores the environment

• The input vector is evaluated : u i (1) ∈ [u i (1)]

• The robot’s new pose : [q i (2)] = f ([q i (1)],[u i (1)])

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Example of set-membership pose tracking

Drifting problem

• The uncertainty increases

• An exteroceptive information is needed

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Summary

1 The Pose Tracking Problem

2 The Visibility Information Definitions

Interval extension of the visibility 3 The LUVIA algorithm

4 Conclusion

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion Definitions

Visibility

Definition

The visibility between two robots r ₁ and r ₂ with their respective positions x ₁ and x ₂ in an environment E is a binary relation noted V such as :

• (x ₁ V x ₂ ) E ⇔ Seg(x ₁ ,x ₂ ) ∩ E = 0 /

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion Definitions

Non-visibility

Definition

The non-visibility between two robots r ₁ and r ₂ with their respective positions x ₁ and x ₂ in an environment E is a binary relation noted V such as :

• (x ₁ V x ₂ ) E ⇔ ¬(x ₁ V x ₂ ) E

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion Interval extension of the visibility

Interval visibility

Definition

Let [x ₁ ] and [x ₃ ] be two boxes, and an environment E

• ([x ₁ ] V [x ₃ ]) E ⇔ ∀x ₁ ∈ [x ₁ ],∀x ₃ ∈ [x ₃ ], (x ₁ V x ₃ ) E

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Interval non-visibility

Definition

Let [x ₂ ] and [x ₃ ] be two boxes, and an environment E

• ([x ₂ ] V [x ₃ ]) E ⇔ ∀x ₂ ∈ [x ₂ ],∀x ₃ ∈ [x ₃ ], (x ₂ V x ₃ ) E

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Partial-visibility

Remark

Let [x ₁ ] and [x ₂ ] be two boxes, and an environment E

• ([x 1 ] V [x 2 ]) E and ([x 1 ] V [x 2 ]) E can be both false

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Summary

1 The Pose Tracking Problem

2 The Visibility Information

3 The LUVIA algorithm

The environment characterization

The visibility/non-visibility test

The algorithm

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The environment characterization

The objectives of the characterization

Why a characterization ?

• The environment is not known perfectly

Our solution

• An inner and an outer characterization

• Sets of interval of segments

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The objectives of the characterization

Why a characterization ?

• The environment is not known perfectly

Our solution

• An inner and an outer characterization

• Sets of interval of segments

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The objectives of the characterization

Why a characterization ?

• The environment is not known perfectly

Our solution

• An inner and an outer characterization

• Sets of interval of segments

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The objectives of the characterization

Why a characterization ?

• The environment is not known perfectly

Our solution

• An inner and an outer characterization

• Sets of interval of segments

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Two characterizations

An environment

• E

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Two characterizations

An inner approximation

• E ⁻ such as E ⁻ ⊂ E

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Two characterizations

An outer approximation

• E ⁺ such as E ⊂ E ⁺

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Two characterizations

Two guaranteed characterizations

• E ⁻ ⊂ E ⊂ E ⁺

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The visibility/non-visibility test

Propositions

Environment and characterizations

• ([x ₁ ] V [x ₂ ]) E ⇒ ([x ₁ ] V [x ₂ ]) E

⁻

• ([x 1 ] V [x 2 ]) E ⇒ ([x 1 ] V [x 2 ]) E

⁺

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The visibility/non-visibility test

Propositions

Environment and characterizations

• ([x ₁ ] V [x ₂ ]) E ⇒ ([x ₁ ] V [x ₂ ]) E

⁻

• ([x 1 ] V [x 2 ]) E ⇒ ([x 1 ] V [x 2 ]) E

⁺

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The algorithm

The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility

information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility

information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility

information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility

information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility

information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility

information and the environment characterizations

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The LUVIA algorithm (Localization Using Visibility and Interval Analysis)

The main idea

• Erase the values that are not consistent with the visibility information and the environment characterizations

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Summary

1 The Pose Tracking Problem

2 The Visibility Information

3 The LUVIA algorithm

4 Conclusion

Simulation results

The perspectives

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion Simulation results

Simulation results

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Simulation results

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Simulation results

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The perspectives

Perspectives

Current work

• Development of a contractor

• To improve the efficiency

• To improve the computation speed

Considered work

• Considering mirror obstacles

• Considering other application fields

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Introduction The Pose Tracking Problem The Visibility Information The LUVIA algorithm Conclusion The perspectives

Mobile Robots Pose Tracking-A Set-membership Approach using a Visibility Information.